Because drainage is such an important thing to consider, please consult with a local expert to at least have a plan drawn up for your yard. If you don't, you could have long-term problems that will be very expensive to fix. That said, if you elect to do the actual work yourself, start by killing all of the grass with a non-selective herbicide like glyphosate (the active ingredient in Roundup). As soon as all of the grass is dead, work organic matter like compost into the soil, down to about 8 inches. Then rake the soil smooth and top dress with mulch, like shredded bark or shredded leaves. Pull apart the mulch to plant the groundcover the recommended distance apart. (Frankly, I like to plant closer together to achieve a more dense effect, more quickly.) Some recommended groundcovers are (check with your local extension service-they'll have a list for your area): Ajuga, Creeping buttercup (Ranunculus repens), Crown vetch, English ivy, Goutweed (Aegopodium podagraria), Honeysuckle, Knotweed (Polygonum spp.) Lily-of-the-valley, Periwinkle (Vinca minor), Sweet woodruff (Gallium odoratum), and Yellow archangel (Lamium galeobdolon). Also, consider some natural grasses (not turf grasses) or those adapted to your area.
